Finding WordPress Posts assigned to multiple categories

I think I’d setup a loop for all posts and the do something like this inside the loop:

$post_cats = get_the_category();
$brand_cats = 0;
$retail_cats = 0;
foreach ( $post_cats as $post_cat ) {
    if ($post_cat->category_parent == 187) {
        $brand_cats++;
    if ($post_cat->category_parent == 186) {
        $retail_cats++;
    }
}
if ( $brand_cats > 1 )
    echo "Duplicate Brand for Post #".get_the_ID;
if ( $retail_cats > 1 )
    echo "Duplicate Retailer for Post #".get_the_ID;

The code is untested but should give you the general approach.